Since entropic regularization leads to efficient numerical schemes and is statistically more appealing (see next Section REF ), it is tempting to use \(\)  off-the-shelf as a loss function for ML or imaging sciences applications.
For instance many learning tasks such as generative learning [1]} or VAE [2]} seek to optimize a parameterized model \(_\)  with parameter \(\in ^d\)  such that it approximates well a data distribution \(_N\) .
To train the model one minimizes
\(\min _{\in ^d} (_,_N) + (_),\) 
